With the US-Israeli war on Iran in its third week, Trump said US strikes had "totally demolished" much of the island and warned of more, telling NBC News on Saturday, "we may hit it a few more times just for fun".
The remarks marked a sharp escalation from Trump, who had previously said the US was targeting only military sites on Kharg, and undercut diplomatic efforts.
His administration has rebuffed efforts by Middle Eastern allies to start negotiations, three sources told Reuters.
The war showed no sign of ending. Trump said Tehran appeared ready to make a deal to end the conflict but that "the terms aren't good enough yet".
Tehran's ability to halt shipping through the Strait of Hormuz, through which one-fifth of the world's oil passes, poses a difficult problem for the US and its allies.
Energy prices are soaring as the war causes the biggest-ever disruption in oil supply, and the energy crisis looks set to continue.
"The Countries of the World that receive Oil through the Hormuz Strait must take care of that passage, and we will help — A LOT!" Trump wrote in a social media post on Saturday.
"The US will also coordinate with those Countries so that everything goes quickly, smoothly, and well."
Iranian Foreign Minister Abbas Araqchi said Iran would respond to any attack on its energy facilities.
Iran's Revolutionary Guards said on Sunday they had carried out missile and drone strikes on targets in Israel and three US bases in the region, calling the attacks the first round of retaliation for workers killed in Iran's industrial areas.
The Israeli military said it was intercepting incoming launches.
Saudi Arabia intercepted and destroyed 10 drones in Riyadh and the east, the defence ministry said.
Iran's Revolutionary Guards said they had no connection to the attack, the semi-official Fars news agency reported.
A drone attack disrupted a major United Arab Emirates energy hub on Saturday, and the US warned US citizens on Saturday to leave Iraq.
The war that Trump and Israeli Prime Minister Benjamin Netanyahu launched on February 28 has killed more than 2000 people, mostly in Iran, according to reports from governments and state media.
At least 15 were killed when an air strike hit a refrigerator and heater factory in the central Iranian city of Isfahan, the semi-official Fars news agency said on Saturday.
Russia is supplying Iran with Shahed drones to use against the US and Israel, Ukrainian President Volodymyr Zelenskiy told CNN.
Shahed drones have been linked to other attacks on countries in the region, although their manufacturers are not always clear.
Oil market disruptions look unlikely to end soon.
Some oil-loading operations were suspended in the UAE's Fujairah emirate, a global ship-refuelling hub, after a drone attack, industry and trade sources said on Saturday.
Trump, in a post on his Truth Social platform, urged China, France, Japan, South Korea, Britain and others to send warships to the Strait of Hormuz.
None of those countries gave any immediate indication they would.
Takayuki Kobayashi, Japan's ruling party policy chief, declined to rule out the possibility, but told public broadcaster NHK "the (legal) threshold is very high".
Japan interprets its pacifist postwar constitution to mean it can deploy its military if the nation's survival is threatened, but the government would have to invoke a 2015 security law that has not been used.
France is seeking to assemble a coalition to secure the Strait of Hormuz once the security situation stabilises, while Britain is discussing a range of options with allies to ensure the security of shipping, officials have said.
Iran's Supreme Leader Ayatollah Mojtaba Khamenei, who replaced his slain father, has said the Strait of Hormuz should remain closed.
